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This paper is a review dealing with the study of large
size random recurrent neural networks. The connection weights are
varying according to a probability law and it is possible to predict
the network dynamics at a macroscopic scale using an averaging
principle. After a first introductory section, the
section 2 reviews the various models from the points of
view of the single neuron dynamics and of the global network
dynamics. A summary of notations is presented, which is quite
helpful for the sequel. In section 3, mean-field dynamics
is developed. The probability distribution characterizing global
dynamics is computed. In section 4, some applications
of mean-field theory to the prediction of chaotic regime for Analog
Formal Random Recurrent Neural Networks (AFRRNN) are displayed. The
case of AFRRNN with an homogeneous population of neurons is studied
in section 4.1. Then, a two-population model is studied in
section 4.2. The occurrence of a cyclo-stationary chaos is
displayed using the results of [16]. In
section 5, an insight of the application of mean-field
theory to IF networks is given using the results
of [9]
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